We numerically demonstrate a broadband terahertz (THz) absorber that is based on a hybrid-patterned graphene metasurface with excellent properties of polarization insensitivity, wide-angle, and active tunability. Our design is made up of a single-layer graphene with periodically arranged hybrid square/disk/loop patterns on a multilayer structure. We find that broadband absorption with 90% terahertz absorbance and the fractional bandwidth of 84.5% from 1.38 THz to 3.4 THz can be achieved. Because of the axisymmetric configuration, the absorber demonstrates absolute polarization independence for both transverse electric (TE) and transverse magnetic (TM) polarized terahertz waves under normal incidence. We also show that a bandwidth of 60% absorbance still remains 2.7 THz, ranging from 1.3 THz to 4 THz, for a wide incident angle ranging from 0° to 60°. Finally, we find that by changing the graphene Fermi energy from 0.7 eV to 0 eV, the absorbance of the absorbers can be easily tuned from more than 90% to lower than 20%. The proposed absorber may have promising applications in terahertz sensing, detecting, imaging, and cloaking.

The higher order mixed spectral-element method (SEM) is proposed for the analysis of anisotropic, lossy, and open waveguides. The new variational formulation incorporating Gauss' law into the vectorial wave equation is completely free of spurious modes. It utilizes the edge-based curl-conforming Gauss-Lobatto-Legendre (GLL) polynomials to approximate the tangential vector of the electric field and the nodal-based scalar GLL basis functions to discretize its longitudinal component to obtain the highly accurate solution. By employing the mass-lumping technique, only a smaller generalized eigenvalue problem needs to be solved. Several numerical examples are given to verify that the mixed SEM is free of any spurious eigenmode and has spectral accuracy with the propagation constant.

The mixed spectral-element method (MSEM) is applied to solve the waveguide problem with the Bloch periodic boundary condition (BPBC). Based on the BPBC for the original Helmholtz equation and the periodic boundary condition (PBC) for the equivalent but modified Helmholtz equation, two equivalent mixed variational formulations are applied for the MSEM. Unlike the traditional finite-element method and spectral-element method (SEM), both these mixed SEM schemes are completely free of spurious modes because of their use of the Gauss’ law and the curl-conforming vector basis functions structured by the Gauss–Legendre–Lobatto points. A simple implementation method is used to deal with the BPBC and the PBC for the mixed variational formulations so that both schemes can save computational costs over the traditional methods. Several numerical results are also provided to verify that both schemes are free of spurious modes and have high accuracy with the propagation constants.

A joint petrophysical and structural inversion method for electromagnetic (EM) and seismic data based on the volume integral equation (VIE) is proposed in this paper. In the forward EM problem, only the contrast of conductivity is solved by the electric field integral equation method. However, in the forward seismic problem, both the contrasts of velocity and mass density are solved by the combined field VIE method. Both forward solvers are accelerated by the fast Fourier transform. In the inversion problem, by using the petrophysical equations about the porosity and saturation and applying the chain rule, we fuse the EM and seismic data and construct the joint petrophysical inversion equations, which can be solved by the variational Born iteration method. Then, in order to further enhance the reconstructed results of the joint petrophysical inversion, we enforce the structural similarity constraint between porosity and water saturation and add the cross-gradient function to the joint petrophysical inversion cost function. Two typical geophysical models based on the remote sensing measurement are used to validate the proposed methods. One is the cross-well model, and the other is the marine surface exploration model. The advantage of the joint inversion compared with the separate inversion is evaluated based on the resolution and the data misfits of the reconstructed profiles as well as the antinoise ability.

The spectral element method (SEM) is a special kind of high-order finite element method (FEM) which combines the flexibility of a finite element method with the accuracy of a spectral method. In contrast to the traditional FEM, the SEM exhibits advantages in the high-order accuracy as the error decreases exponentially with the increase of interpolation degree by employing the Gauss–Lobatto–Legendre (GLL) polynomials as basis functions. In this study, the spectral element method is developed for the first time for the determination of band structures of 3D isotropic/anisotropic phononic crystals (PCs). Based on the Bloch theorem, we present a novel, intuitive discretization formulation for Navier equation in the SEM scheme for periodic media. By virtue of using the orthogonal Legendre polynomials, the generalized eigenvalue problem is converted to a regular one in our SEM implementation to improve the efficiency. Besides, according to the specific geometry structure, 8-node and 27-node hexahedral elements as well as an analytic mesh have been used to accurately capture curved PC models in our SEM scheme. To verify its accuracy and efficiency, this study analyses the phononic-crystal plates with square and triangular lattice arrangements, and the 3D cubic phononic crystals consisting of simple cubic (SC), bulk central cubic (BCC) and faced central cubic (FCC) lattices with isotropic or anisotropic scatters. All the numerical results considered demonstrate that SEM is superior to the conventional FEM and can be an efficient alternative method for accurate determination of band structures of 3D phononic crystals.